To solve the original inequality 3x + 5 < 10, we first isolate x.
1. Start by subtracting 5 from both sides of the inequality:
3x + 5 – 5 < 10 – 5
3x < 5
2. Next, we divide both sides by 3 to isolate x:
x < rac{5}{3}
So far, we have x < rac{5}{3}. However, if we consider a situation where we might have an inequality such as 3x + 5 > -10, we can also set up a compound inequality.
3. To create this compound inequality, we write:
-10 < 3x + 5 < 10
4. Now, we solve using the two sides of the compound inequality:
For the left side:
-10 < 3x + 5
ightarrow -10 – 5 < 3x
ightarrow -15 < 3x
ightarrow -5 < x
For the right side:
3x + 5 < 10
ightarrow 3x < 5
ightarrow x < rac{5}{3}
5. Combining both results gives us:
-5 < x < rac{5}{3}
This is the compound inequality that can be used to solve the original inequality 3x + 5 < 10. It provides the range of values for x that satisfy both sides of the inequality, making it a useful approach in understanding the solution set clearly.